The problem
I had a problem with a fresh wp 2.8.6 install which I've seen multiple other people complaining about. When you upload an image in the media uploader everything seems to be alright but the picture is broken when you save.
The reason
After some searching I found that the images were uploaded to wp-content but the links pointed to wp-content/uploads/
The solution
In the admin interface go to settings then to Miscellaneous. There you should change the value to "wp-content/uploads". This should be the default value but is appearantly not. Now everything will work great.
The conclusion
This should definitely be fixed by the wordpress in case it is not just a mistake on my part of some kind. However I downloaded the package twice and did complete installs both times by first removing and then uploading the new files.